Ben that is a fascinating snippet! Thank you.
I think what the snippet shows is that it's worth bearing in mind that
Peirce's paper on logical comprehension and extension was very early - 1867
- and here he is still working in a 'finitist' tradition in metaphysics and
logic, which he manages to shake himself free of in his later
synechism. Under synechism every real object has an infinite number of
attributes, and every meaningful predicate or general term effectively has
an infinite number of aspects, so a simple multiplication of B x D is
pointless.
And now for what I think is the answer to the question I posed:
*QUESTION: How does Peirce attempt to draw the distinction, in the two
cases Frederik catalogues?*
The examples Peirce gives of a natural and artificial class are*
cows*, and *red
cows* respectively.
I think what he thinks distinguishes the two is that the latter, being
arbitrarily defined, has no further properties than those already
enumerated in the definition. So all we can say about the class of red cows
is that they are cows and they are red.
Whereas the natural class can be inquired into further indefinitely. The
class of cows all share - a certain DNA, certain feeding habits, certain
reproductive strategies, etc. Now I suppose one might argue that the class
of red cows has all those properties too, because the red cows are cows.
But I guess the key point is that there is no EXTRA determination being
given by the redness. Whereas if we said, all *Jersey* cows, the
Jerseyness would have certain further characteristics which can be studied,
and thus this is a natural class.
So with the drawings, I think Peirce is trying to make it that case
that certain of the repeatable drawing features covary with certain other
of the features, and not with others, in ways such that we can capture the
minimal structure necessary for us to be able to group the features
together into 'artificial' and 'natural' classes. So the artificial ones
are those where features A and B go together in a series of cases, but no
other features are shared there. The natural ones are ones where features A
and B go together and in those cases are accompanied by further features C
and D.
All this reminds me of a passage I was writing in a paper but then took out
before publication. It is trying to give a minimal definition of
*scholastic realism*, and arguing that it is not ruled out by fiat as
certain Humean picture in philosophy suggests. I reproduce it below in
case anyone is interested.
And here ends my postings on Chapter 9!
Cheers, Cathy
Hume’s maxim [i.e. 'there are no necessary connections between distinct
existences', 'the only contraries and existence and non-existence' - CL] ,
and associated Modal Combinatorialism, can be usefully summed up as a
*syntactic
approach to modality*. To argue this, let us frame the issue in maximally
general terms. Consider a world consisting of 4 ‘idea / objects’ (*a*, *b*,
*c* and *d*) – which may combine to make larger states of affairs. Imagine
that these idea / objects are all *distinguishable*. Then according to Hume
they must be *separable*. Let us now imagine a toy universe in which the
only contraries are existence and non-existence. In such a universe
ontologically there may exist - and epistemologically we may imagine - all
possible ‘combinations’ of the objects (just one simple two-way combination
is illustrated for purposes of simplicity, represented by the names of our
objects appearing to the left or right of each other):
*aa ab ac ad ba bb bc bd ca cb cc cd da db dc dd…*
Let us now imagine a toy universe in which Modal Combinatorialism is false.
This just means that not all combinations are realisable. Here is just one
example:
*aa ab ad ba bb bd ca cb cc cd da db dd…*
This toy universe is missing *ac*, *bc* and *dc*, (for some reason, let us
imagine it is to do with the nature of *c*). An intelligent mind inspecting
the world above might think to summarise the combinations missing from it
in a simple statement – something like, ‘*c* can never come last in
combination, unless with another *c*’. This statement is obviously a
rudimentary law, or universal.
Our point is now merely that the second scenario is not incoherent. It
is not analytically false to conceive extra-logical constraints on the
happy combination of any conceivable object with any other conceivable
object (bearing in mind that of course these objects will have
*natures*). Mathematics...rules
out such combinations regularly: for example, the combination of 2 × 3 with
3 × *x*, for any *x *other than 2. Hume’s Modal Combinatorialism is
therefore a way of killing off a kind of realism about universals without
being honest about it.
------------------------------
On Mon, Mar 9, 2015 at 1:21 AM, Benjamin Udell <bud...@nyc.rr.com> wrote:
> Cathy, list,
>
> You wrote,
>
> QUESTIONS: In what sense, and to what degree might this 'information' be
> measured? (If not in some absolute sense, then perhaps relatively, between
> propositions?) Doesn't the very notion of measuring this value conflict
> with Peirce's contrite fallibilism, which holds that what a given term will
> come to mean to us is not something that can be decided in advance of
> scientific inquiry? In other words, scientific terms can hold a great deal
> of implicit information as well as the explicit information that scientists
> are working with at a given time.
> [End quote]
>
> Presumably the information to be quantified is not that of what a given
> term will come to mean to us, but rather that of what it means to us now -
> the difference between making our ideas true, as Peirce put it, and making
> our ideas clear. What it means to us now is what we now conceive to be its
> practical bearing in general on conduct.
>
> I have to admit I have little to say about how to quantify comprehension,
> denotation, information in Peirce's sense. I did find this passage:
>
> Writings 1:342-343, Logic Notebook Dec. 15, 1865
>
> http://pds.lib.harvard.edu/pds/view/15255301?n=28&imagesize=600&jp2Res=0.25&printThumbnails=true
>
> In the formula
>
> Extension × Intension = Implication
>
> we may have the values
>
> (1) 0 × 0 = 0
> (2) 0 × n = 0
> (3) 0 × ∞ = 0
> (4) 0 × ∞ = n
> (5) 0 × ∞ = ∞
> (6) n × 0 = 0
> (7) n × n = n
> (8) n × ∞ = ∞
> (9) ∞ × 0 = 0
> (10) ∞ × 0 = n
> (11) ∞ × 0 = ∞
> (12) ∞ × n = ∞
> (13) ∞ × ∞ = ∞
>
> (7) will be the case with any ordinary symbol.
>
> (4) is the ordinary nothing.
>
> (10) the ordinary being.
>
> These are the cases when Implication is n. Now for those where it is 0.
>
> (6) is the case of a sign, (2) of a copy.
>
> (1) would be a sign of nothing or a copy of being which are undetermined
> to be representations.
>
> (9) would be being supposing it were not known to be, or being considered
> abstractly of the fact that it is.
>
> (3) would be nothing abstracting from the fact that there is anything so
> that its opposition is taken away.
>
> A being which isn't, would be a nothing which is unopposed to anything;
> hence being abstracted from the fact that it is is abstracted from all that
> makes it differ from nothing abstracted from its opposition and vice versa.
>
> We will now take up the cases where the implication = ∞. (12) is being of
> which some determinate quality is supposed to be known.
>
> (8) is a contradiction it being implied that it exists.
>
> (13) is being which is supposed to have all attributes.
>
> (11) would purport to be a complete list of all beings.
>
> (5) would purport to be a complete conjunction of all attributes.
> [End quote]
>
> You wrote,
>
> QUESTION: How does Peirce attempt to draw the distinction, in the two
> cases Frederik catalogues?
> [End quote]
>
> I can't think of anything to say about this either, though the question of
> natural vs. artificial kinds is quite interesting to me. Similar question
> in mathematics: Are primes a natural kind? What about the class of
> functions that share a certain first derivative? The class of pairs of
> integers that sum to a certain integer?
>
> You wrote,
>
> List: if you tell me what you think then I will tell you what I think.
> [End quote]
>
> I haven't done too well, nobody else has replied, I guess you ask tough
> questions, but anyway at this point I'm interested in hearing what you
> think.
>
> Best, Ben
>
> On 3/3/2015 2:41 PM, Catherine Legg wrote:
>
> Picking up again where I left off...
> The logical tradition that Peirce was responding to with his
> piece "Logical Extension and Comprehension" was basically a 'term logic',
> according to which this rough formula held:
>
> Breadth x Depth = k (where k is some constant)
>
> This implies: the larger the extension (breadth), the smaller the
> intension (depth). This formula seems to work for classic terms such as
> "blue", which covers more things but is correspondingly less precise than,
> say, "baby blue". Or "vehicle" which covers more things but is less precise
> than, say "nuclear submarine".
>
> However, Peirce's shift from terms to propositions as a basic analysis of
> meaning allows him to question some of this framework. A proposition is now
> not a simple 'multiplication' of two 'similar quantities'. A proposition
> requires two separate functionalities. The part which provides the
> extension (the subject) functions indexically, and the part which provides
> the intension (the predicate) functions iconically.
>
> Stjernfelt points out that, under this framework, "far from being a
> constant, Breadth x Depth gives a measure of the amount of information
> inherent in a proposition" (which can be higher or lower). He notes that
> Peirce still retained this idea 25 years later in Kaina Stoicheia.
>
> *QUESTIONS: In what sense, and to what degree might this 'information'
> be measured? (If not in some absolute sense, then perhaps relatively,
> between propositions?) Doesn't the very notion of measuring this value
> conflict with Peirce's contrite fallibilism, which holds that what a given
> term will come to mean to us is not something that can be decided in
> advance of scientific inquiry? In other words, scientific terms can hold a
> great deal of implicit information as well as the explicit information that
> scientists are working with at a given time. *
>
> Probably in the light of this kind of worry, Peirce sets himself the task
> to trying to analytically define what is a 'natural class'. For natural
> classes are precisely those which bear future inquiry, yielding up implicit
> information to be made explicit. As Peirce says, think how much more
> "electricity" means now than in the days of Dalton. Whereas an a
> non-natural ("artificial") class - has nothing more to tell us apart from
> the way it was already defined. Peirce gives the example of 'cow' as a
> natural class and 'red cow' as artificial.
>
> To this end, he draws two sets of mysterious diagrams, as a kind of
> experiment, possibly unfinished. This seems to be an experiment in defining
> "properties" or "marks" in the most minimal way possible, then varying them
> in the most minimal ways possible, to try to decide what groupings our
> scientific inquirer might decide are 'natural'. This is not a simple matter
> of making a class for each property, as we do not have a distinction
> between natural and artificial classes.
>
> *QUESTION: How does Peirce attempt to draw the distinction, in the two
> cases Frederik catalogues?*
>
> List: if you tell me what you think then I will tell you what I think.
>
> Cheers, Cathy
>
> On Tue, Feb 24, 2015 at 10:12 PM, Catherine Legg wrote:
>
>
>
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